Internal problem ID [13409]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.10 (g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=\sin \left (x \right ) {\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=exp(2*x)*sin(x),y(x), singsol=all)
\[ y = {\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (x \right ) c_{1} +\frac {{\mathrm e}^{2 x} \left (\sin \left (x \right )-\cos \left (x \right ) x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 30
DSolve[y''[x]-4*y'[x]+5*y[x]==Exp[2*x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{2} e^{2 x} ((x-2 c_2) \cos (x)-2 c_1 \sin (x)) \]